Manufacturing of unidirectional glass-fiber-reinforced composites via frontal polymerization: A numerical study
Introduction
Due to their high specific strength and stiffness, flexibility and resistance to chemical harm, glass-fiber-reinforced polymer composites (GFRPCs) are found in many structural applications in the aerospace, marine, wind energy, and automotive industries [1]. However, traditional manufacturing processes of composite materials based on autoclaves and heated molds require significant capital investments and have high energy requirements associated with the complex and time-consuming cure cycles involved in the bulk curing of the thermosetting resin [2]. A recently introduced alternative to conventional manufacturing techniques, frontal polymerization (FP), which involves a highly localized and self-propagating exothermic reaction zone converting a monomer into a polymer [[3], [4], [5], [6], [7]], offers a cheaper, faster, and energy-efficient option for manufacturing composites [8].
Multiple mathematical models have been introduced to describe frontal polymerization in a variety of chemicals. Goldfeder et al. [9] and Solovyov et al. [10] used a free-radical polymerization model to solve for the degree of conversion of the monomer to polymer coupled with the heat diffusion equation to describe the process of FP in butyl acrylate and methacrylic acid, respectively. Instead of solving for the conversion of the monomer, phenomenological models based on a cure kinetics relation can be used to simplify the mathematical model [11]. In this line of work, Frulloni et al. [12] developed a finite difference model to describe FP in an epoxy system. Recently, Robertson et al. [8] and Goli et al. [13] used the finite element method to solve the transient, coupled diffusion-reaction equations based on the Prout-Tompkins model [14] to describe FP in DCPD.
In this study, we use the reaction-diffusion relations described in Ref. [8] and homogenize this model to incorporate the effects of the glass fibers on the frontal polymerization of glass/DCPD composites. Using an open-source transient finite element solver, we conduct a detailed parametric study using 1-D simulations to study the effects of the glass fibers on the velocity, width and maximum temperature of the reaction front. We also develop a semi-analytic steady-state formulation, which converts the coupled reaction-diffusion partial differential equations to a system of ordinary differential equations [13], compare the steady-state results to those obtained with the transient finite element solver and use the steady-state solver to quantify the dependence of the front speed on the heat of the reaction.
The present study on glass/DCPD composites builds on the recent work of Robertson et al. [8] and Goli et al. [15], who investigated both experimentally and numerically the feasibility of FP-based manufacturing of carbon/DCPD composites. To demonstrate the importance of the thermal conductivity of the reinforcing phase alluded to recently in Ref. [16], we also compare the glass/DCPD results to the carbon/DCPD predictions obtained by Goli et al. [15].
The manuscript is organized as follows: The transient and steady-state formulations of the homogenized reaction-diffusion thermo-chemical model used to describe the propagation of a polymerization front in a unidirectional composite are summarized in Sections 2 Transient reaction-diffusion model, 3 Steady-state formulation, respectively. Results from these two models for glass/DCPD composites are presented in Section 4, with emphasis on the effect of the fiber volume fraction on the speed, temperature and intrinsic length scales of the polymerization front. Section 5 compares the characteristics of the polymerization front in glass/DCPD and carbon/DCPD composites.
Section snippets
Transient reaction-diffusion model
In the present study, the cure kinetics of FP in DCPD is described using the Prout-Tompkins autocatalytic model with diffusion effects [13]. To simulate the presence of glass fibers in the unidirectional E-glass-fiber-reinforced DCPD composite, we modify the thermal diffusion model by homogenizing the thermal properties of the material. Assuming adiabatic conditions, i.e., in the absence of heat losses to the surrounding, the homogenized reaction-diffusion equations in terms of the temperature T
Steady-state formulation
To capture the steady-state propagation of the reaction front, we convert the coupled, partial differential equations to a system of coupled, ordinary differential equations (ODEs) by rewriting the temperature and degree of cure solution in a coordinate frame moving with a steadily propagating polymerization front [13]. This method serves as a more efficient alternative to study the impact of the reinforcing phase and of the cure kinetics on the key characteristics (speed, width and maximum
Results
The resin of interest in this study is DCPD mixed with Grubb's 2nd-generation catalyst and 0.5 molar equivalent of tri-butyl phosphite, an inhibitor introduced to increase the pot life of the monomer [8]. The material properties (including the diffusivity λ) considered in this study are presented in Table 1, while the cure kinetics parameters for the DCPD resin are presented in Table 2.
In all finite element simulations, the solution for the temperature and degree of cure goes first through a
Comparison between glass/DCPD and carbon/DCPD composites
In a recent study, Goli et al. [15] have shown that FP is a viable manufacturing method for unidirectional carbon-fiber-reinforced DCPD-matrix composites. The authors implemented a similar reaction-diffusion model to perform simulations of the initiation and propagation of the front in carbon/DCPD composites, and validated the model against experimental measurements of the front speed and temperature obtained for various values of the fiber volume fraction.
In this section, we present a
Conclusion
In this paper, we have explored numerically the feasibility of frontal polymerization as a manufacturing process for E-glass-fiber-reinforced composites. The frontal polymerization process has been described by a system of coupled thermo-chemical equations, with the effects of the reinforcing phase captured through homogenized thermal properties and through a reduction in the available heat of reaction. The effects of the fiber volume fraction on the velocity, width and maximum temperature of
Acknowledgement
This work was supported by the Air Force Office of Scientific Research through Award FA9550-16-1-0017 (Dr. B. ‘Les’ Lee, Program Manager) as part of the Center for Excellence in Self-Healing, Regeneration, and Structural Remodeling. This work was also supported by the National Science Foundation (NSF Grant No. 1830635), through the LEAP HI: Manufacturing USA program. The authors would like to acknowledge Prof. Scott White for his insights and guidance regarding this work.
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2022, Additive ManufacturingCitation Excerpt :Frontal polymerization (FP) is a novel curing strategy that relies on a self-propagating exothermic reaction front to polymerize thermoset resins rapidly[19–21]. Due to its energy-efficiency and rapid curing of thermosets, FP has been used to develop a series of applications related to polymer and polymer composites manufacturing [22–27]. Another notable advantage of FP is its great compatibility with other manufacturing processes, such as ultrasound-assisted FP and concurrent polymerization and vascularization [28].
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Current address: Department of Mechanical Engineering, University of Wyoming, Laramie, WY, 82071, United States.